Line fitting (least square method)

Linear equation ：
$$y=ax+b$$
A set of data is obtained from the experimental test , Write it down as ：$$(x_i,y_i)$$
Now we need to use the test data , Find the parameters of the linear equation a, b Make the straight line most consistent with the experimental data , Which is equivalent to the problem ：
$$\underset{a,b}{\min }\Sigma [y_i-(a{x}_i+b){]}^2$$
remember ：
sum=$\Sigma [y_i-(a{x}_i+b){]}^2$
Yes a, b Derivation ：
$$\frac{dsum}{da}=\Sigma \{-2x_i[y_i-(a{x}_i+b)]\}=0$$
$$\frac{dsum}{db}=\Sigma \{-2[y_i-(a{x}_i+b)]\}=0$$
So we can get ：
$$a=\frac{n\Sigma x_i{y}_i-\Sigma x_i\Sigma y_i}{n\Sigma x_i^2-(\Sigma x_i{)}^2}$$
$$b=\frac{\Sigma y_i-a\Sigma x_i}{n}$$
among ,n The total number of data obtained for the test .
When $n\Sigma x_i^2-(\Sigma x_i{)}^2=0$ when , The slope of the line a To be big for nothing , non-existent , here , The linear equation is ：
$$x=(\Sigma x_i)/n$$

Resources for a,b The result of the coefficient is reversed , Therefore, the formula is reorganized .

Reference material ：
https://wenku.baidu.com/view/d4ede28a910ef12d2af9e7e1.html